28 citations · 187 across the 25 of their papers we have counts for
8 papers · 1 filter
CoBarS: Fast reweighted sampling for polygon spaces in any dimension
Jason Cantarella, Henrik Schumacher
We present the first algorithm for sampling random configurations of closed -gons with any fixed edgelengths in any dimension which is proved to sample cor…
Square-like quadrilaterals inscribed in embedded space curves
Jason Cantarella, Elizabeth Denne, John McCleary
The square-peg problem asks if every Jordan curve in the plane has four points which are the vertices of a square. The problem is open for continuous Jordan curves, but it has been…
Computing the conformal barycenter
Jason Cantarella, Henrik Schumacher
The conformal barycenter of a point cloud on the sphere at infinity of the Poincaré ball model of hyperbolic space is a hyperbolic analogue of the geometric median of a point cloud…
The symplectic geometry of closed equilateral random walks in 3-space
Jason Cantarella, Clayton Shonkwiler
A closed equilateral random walk in 3-space is a selection of unit length vectors giving the steps of the walk conditioned on the assumption that the sum of the vectors is zero. Th…
The Expected Total Curvature of Random Polygons
Jason Cantarella, Alexander Y Grosberg, Robert B. Kusner +1
We consider the expected value for the total curvature of a random closed polygon. Numerical experiments have suggested that as the number of edges becomes large, the difference be…
Symmetric Criticality for Tight Knots
Jason Cantarella, Jennifer Ellis, Joseph H. G. Fu +1
We prove a version of symmetric criticality for ropelength-critical knots. Our theorem implies that a knot or link with a symmetric representative has a ropelength-critical configu…
Probability Theory of Random Polygons from the Quaternionic Viewpoint
Jason Cantarella, Tetsuo Deguchi, Clayton Shonkwiler
We build a new probability measure on closed space and plane polygons. The key construction is a map, given by Knutson and Hausmann using the Hopf map on quaternions, from the comp…
On comparing the writhe of a smooth curve to the writhe of an inscribed polygon
Jason Cantarella
We find bounds on the difference between the writhing number of a smooth curve, and the writhing number of a polygon inscribed within. The proof is based on an extension of Fuller'…